Question: Reduce to lowest terms: $ \dfrac{7}{2} \div - \dfrac{3}{7} = {?}$
Solution: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{3}{7}$ is $- \dfrac{7}{3}$ Therefore: $ \dfrac{7}{2} \div - \dfrac{3}{7} = \dfrac{7}{2} \times - \dfrac{7}{3} $ $ \phantom{ \dfrac{7}{2} \times - \dfrac{7}{3}} = \dfrac{7 \times -7}{2 \times 3} $ $ \phantom{ \dfrac{7}{2} \times - \dfrac{7}{3}} = \dfrac{-49}{6} $